remainder theorem long division. long division question divide the following
TRANSCRIPT
Remainder Theorem
Long Division
Long Division QuestionDivide the following
)3(524 23 xxxx
Long Division
5243 23 xxxx
How many times does x go into x3 ?2x Multiply x-3 by x2 .
23 3xx
Subtract down. Note 4x2 – (-3x2)=4x2 + (+3x2)=7x2
27x
Bring down +2x.
x2How many times does x go into 7x2 ?
x7
xx 217 2 Multiply x-3 by 7x.Subtract down.
x23 5 Bring down –5.How many times does x go into 23x ?
23
Multiply x-3 by 23.6923 x
Subtract down.64
See textbook pg 85 for Computer Algebra System division
Synthetic Division
3 1 4 2 -5
1
3
7
21
23
69
6464)237)(3(524 223 xxxxxxThe division statement is:
To find the remainder without doing the division we could substitute 3 into the function.
You try one (see Notebook)
Remainder Theorem•When a function f(x), is divided by x – k
•the remainder is f(k)
Example 1
1 x b)
2- x a)
by divided is
362when xremainder theDetermine 23
xx
362x)(Let a) 23 xxxf
3)2(6)2(2(2))2( 23 f
153128-8)2( f
15. isremainder theSo
362x)(Let b) 23 xxxf
3)1(6)1(2(-1))1( 23 f-636-2--1)1( f
6.- isremainder theSo
Example 2
. of value theFind 3. isremainder the
2)-(xby divided is 74When 23
m
xmxx
74 )(Let
:Solution23 xmxxxf
7)2(4)2()2( )2(
3)2( that states theoremremainder The23
mf
f
7848 )2( mf
234 )2( mf
3234
3 )2(Set
m
f
5m